2x^2-8x-90=x

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Solution for 2x^2-8x-90=x equation:


Simplifying
2x2 + -8x + -90 = x

Reorder the terms:
-90 + -8x + 2x2 = x

Solving
-90 + -8x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-90 + -8x + -1x + 2x2 = x + -1x

Combine like terms: -8x + -1x = -9x
-90 + -9x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-90 + -9x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-45 + -4.5x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -4.5x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -4.5x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -4.5x + x2 = 0 + 45
-4.5x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-4.5x + x2 = 45

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 45 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 45 + 5.0625

Combine like terms: 45 + 5.0625 = 50.0625
5.0625 + -4.5x + x2 = 50.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 50.0625

Calculate the square root of the right side: 7.075485849

Break this problem into two subproblems by setting 
(x + -2.25) equal to 7.075485849 and -7.075485849.

Subproblem 1

x + -2.25 = 7.075485849 Simplifying x + -2.25 = 7.075485849 Reorder the terms: -2.25 + x = 7.075485849 Solving -2.25 + x = 7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 7.075485849 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.075485849 + 2.25 x = 7.075485849 + 2.25 Combine like terms: 7.075485849 + 2.25 = 9.325485849 x = 9.325485849 Simplifying x = 9.325485849

Subproblem 2

x + -2.25 = -7.075485849 Simplifying x + -2.25 = -7.075485849 Reorder the terms: -2.25 + x = -7.075485849 Solving -2.25 + x = -7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -7.075485849 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.075485849 + 2.25 x = -7.075485849 + 2.25 Combine like terms: -7.075485849 + 2.25 = -4.825485849 x = -4.825485849 Simplifying x = -4.825485849

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.325485849, -4.825485849}

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